a number line shows the ages (in years) that people go to two different movies.

Question

movie 1
1 1 0 3 1 1 2 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
movie 2
0 1 0 0 1 0 2 0 1 0 2 1 1 2 0 0 3 0 1 1 0 1 0 1 1 0 1
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The dot plots show the ages, in years, of people watching two movies at a local theater. Find the median age of the people who watched each movie.

The median age of the people who watched Movie 1 is __.
The median age of the people who watched Movie 2 is __.

find the correct answer for both answers

Answer 1

To find the median age for each movie, we need to follow these steps:

1. List the ages for each movie based on the frequencies provided.
2. Count the total number of people for each movie to find the middle value.
3. Determine the median value from the ordered list.

Movie 1

The age frequencies for Movie 1 are as follows:

• 17 years: 1
• 18 years: 1
• 19 years: 0
• 20 years: 3
• 21 years: 1
• 22 years: 1
• 23 years: 2
• 24 years: 0
• 25 years: 1
• 26 years: 1
• 27 years: 0
• 28 years: 1
• 29 years: 1
• 30 years: 0
• 31 years: 0
• 32 years: 1
• 33 years: 1
• 34 years: 0
• 35 years: 1
• 36 years: 1
• 37 years: 0
• 38 years: 1
• 39 years: 1
• 40 years: 0
• 41 years: 1
• 42 years: 0
• 43 years: 1

To total the counts:

• Total = 1 + 1 + 0 + 3 + 1 + 1 + 2 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 1 + 0 + 0 + 1 = 28 people.

Finding the median for Movie 1:

• The median is the average of the 14th and 15th ages (since \(28/2 = 14\)).
• Listing ages:
  • 17, 18, 20, 20, 20, 21, 22, 23, 23, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 38, 39, 41, 42, 43.

Identifying the 14th and 15th ages:

• The 14th age is 30.
• The 15th age is 31.

Calculating the median: \[ \text{Median} = \frac{30 + 31}{2} = 30.5. \]

Movie 2

The age frequencies for Movie 2 are as follows:

• 24 years: 0
• 25 years: 1
• 26 years: 0
• 27 years: 0
• 28 years: 1
• 29 years: 2
• 30 years: 0
• 31 years: 1
• 32 years: 0
• 33 years: 2
• 34 years: 1
• 35 years: 1
• 36 years: 0
• 37 years: 0
• 38 years: 3
• 39 years: 0
• 40 years: 1
• 41 years: 1
• 42 years: 0
• 43 years: 1
• 44 years: 0
• 45 years: 1
• 46 years: 0
• 47 years: 0
• 48 years: 0
• 49 years: 1
• 50 years: 0

Total = 0 + 1 + 0 + 0 + 1 + 2 + 0 + 1 + 0 + 2 + 1 + 1 + 0 + 0 + 3 + 0 + 1 + 1 + 0 + 1 + 0 + 0 + 0 + 1 = 21 people.

Finding the median for Movie 2:

• The median is the 11th age (since there are 21 people, \((21+1)/2 = 11\)).
• Listing ages:
  • 25, 28, 29, 29, 31, 33, 33, 34, 35, 38, 38, 38, 40, 41, 42, 43, 45, 49.

Identifying the 11th age:

• The 11th age is 38.

Summary of Medians

• The median age of the people who watched Movie 1 is 30.5.
• The median age of the people who watched Movie 2 is 38.

Thus:

• The median age of the people who watched Movie 1 is 30.5.
• The median age of the people who watched Movie 2 is 38.